Analytical solutions and stability of periodic attitude motions of gyrostat spacecrafts in weakly elliptical orbits

This paper investigates the periodic attitude motion of a gyrostat spacecraft in weakly elliptical orbits, focusing on the derivation of approximate analytical solutions and their stability. Unlike circular orbits, which allow for three types of regular precession, elliptical orbits are limited to cylindrical precession. Notably, the research identifies stable periodic attitude motions with the period matching the orbital period near hyperbolic precession in weakly elliptical orbits. The approximate analytical solutions for these periodic motions are derived and validated through numerical simulations of the spacecraft's nonlinear attitude dynamics. Stability analysis reveals that non-resonant scenarios yield stable periodic attitude motions, while internal and combination resonances may induce instability. These findings provide valuable insights for the design of spacecraft systems, enhancing energy-efficient attitude control essential for long-duration missions and optimizing operational performance in various aerospace applications. By leveraging the natural stability of periodic motions in elliptical orbits, this approach has the potential to enhance control accuracy, reduce energy consumption, and extend mission lifespans.